You've never heard the word day used in reference to an epoch? I quote the 12th definition at dictionary.com: "period of existence, power, or influence". So, a day CAN be interpreted differently.
The claim isn't that the Bible was somehow transcribed from some ancient stenographer, but rather that it was inspired by God. In non-spiritual terms, this would be saying that the authors of the Bible had ideas that they then wrote down. The religious belief is that those ideas were divine truth. In my explanations for how the divine is manifested in our universe, we could just as easily say that the belief is that these ideas were realized to be true before they could be scientifically proven.
So, with that foundational understanding in place, these ideas would still be restricted by other technological or exploratory limitations of the day (again, I'm not referring to a 24-hr period
). Case in point: 'the earth', or 'the known lands'. Noah didn't even know what a planet or globe was. Why would anyone think that is what he was referring to (or rather, Moses - who no doubt receive it by verbal tradition). Given that he couldn't possibly be referring to the entire planet, one SHOULD read that entire section as referencing the whole of what they knew - or perhaps that everything was flooded as far as the eye could see. And for THAT we have archaeological evidence.
And finally, where does it say flowers came before trees?